Method of determining delivery flow or delivery head

ABSTRACT

A torque required to achieve the modulated reference speed or adjustment of a modulated torque and the actual speed of the centrifugal pump is determined. Then a model speed is calculated with the aid of a mathematical pump-motor model simulating the behavior of the centrifugal pump within a hydraulic system as well as a disturbance signal from a deviation of the model speed from the actual speed of the centrifugal pump. Then a correction signal is determined by integrating the product of the disturbance signal and a sine or cosine signal with a multiple of the excitation frequency over at least one period of the excitation signal. Finally, at least one model parameter of the pump-motor model is determined as a function of the correction signal and the flow rate and/or the head is calculated using the adapted pump-motor model.

FIELD OF THE INVENTION

The invention relates to a method of determining the delivery flowand/or the delivery head of a speed-controlled centrifugal pump in ahydraulic pipeline network from a system response of the pipelinenetwork detectable in the centrifugal pump to a periodic modulation ofthe speed and/or torque of the centrifugal pump.

Furthermore, the invention relates to a centrifugal pump comprising acentrifugal pump, an electric motor driving it and control electronicsfor controlling the electric motor with or without feedback and set upto carry out the method.

BACKGROUND OF THE INVENTION

U.S. Pat. No. 10,184,476 describes how to stimulate a pipeline networkby periodically modulating the setpoint speed or torque of a centrifugalpump in the pipeline network to provoke a system response that in turnis reflected in an evaluable response of the centrifugal pump, forexample in the form of a change in the electrical power consumption orthe torque required to maintain the (modulated) setpoint speed. Thesystem response (magnitude, shape, phase, deceleration) depends on theso-called “hydraulic impedance” of the piping network. From the responseof the centrifugal pump to this, it can determine its flow rate.

Investigations have shown that this method requires a comparativelylarge modulation amplitude to obtain a sufficiently high signal-to-noiseratio in the useful signal to be evaluated and thus enable reliabledetermining the volume flow and/or the delivery head. In contrast, thenoise in the useful signal is comparatively high at a low modulationamplitude and thus worsens the accuracy of the volumetric flowdetermination. However, a large modulation amplitude leads to flow noisethat is undesirable in pipe networks such as central heating systems orcooling systems.

SUMMARY OF THE INVENTION

The object of the present invention is to improve the method known inthe prior art, in particular to reduce the noise in the useful signaldespite a comparatively low excitation amplitude and at the same time toincrease the accuracy of the determining the flow rate.

SUMMARY OF THE INVENTION

According to the invention, a periodic excitation signal of a certainexcitation frequency is applied to a reference speed or torque of thecentrifugal pump to obtain a modulated reference speed, and then toperform the following steps:

-   a. Determining and adjusting a torque required to achieve the    modulated reference speed or adjusting the modulated torque,-   b. Determining the actual speed of the pump,-   c. Calculating a model speed with the aid of a mathematical    pump-motor model simulating the behavior of the centrifugal pump    within a hydraulic system,-   d. Calculating at least one fault signal from a deviation of the    model speed from the actual speed of the centrifugal pump,-   e. Determining at least one correction signal by integrating the    product of the disturbance signal and a sine or cosine signal with    the single or a multiple of the excitation frequency over at least    one period of the excitation signal,-   f. Adaptation of at least one model parameter of the pump-motor    model as a function of the correction signal, and-   g. Calculating the flow rate and/or the head using the adapted    pump-motor model.

Furthermore, a centrifugal pump with a centrifugal pump, an electricmotor driving it and control electronics for controlling with or withoutfeedback the electric motor is proposed, the control electronics beingset up to carry out the method according to the invention.

The above-described method has numerous advantages. First, it improvesthe accuracy of the flow and/or head determination by counteractingdisturbing influences on the system formed by the centrifugal pump andthe connected hydraulic piping network, thereby reducing the noise inthe determined flow and/or head signal. As a result, the signal requiresless filtering, allowing a faster response of the centrifugal pumpassembly to system condition changes or disturbances in the hydraulicpiping network. Further, the periodic excitation signal may use a lowerexcitation amplitude than in the prior art, thereby reducing noise. As aresult of the adjusting the model parameter during operation of thepump, any modelling inaccuracies in the pump-motor model which may bedue to a scattering of the model parameters in series production and/orto wear due to ageing, for example of the bearings of the centrifugalpump, are also compensated for.

By repeatedly adjusting the model parameter(s), the pump-motor model isdynamic. This allows, among other things, to detect signs of ageing onthe centrifugal pump and to compensate for a resulting error in thepump-motor model that increases over time. In this way, the accuracy ofthe flow rate and/or head determination is kept constantly high over theentire operating time of the pump. In addition, deposits on theimpeller, e.g. of iron oxide, commonly known as “clogging,” can bedetected, thus providing an early indication of the need formaintenance, especially of the overall system.

Suitably, the pump-motor model comprises at least a first equationenabling calculating the flow rate and a second equation enablingcalculating the model speed. Suitably, these two equations arerepeatedly evaluated cyclically. In terms of signals, this calculationcan be performed in parallel.

For example, the first equation may be a flow equation in integral form.It is preferably based on a hydraulic differential equation that inparticular describes a head or pressure balance (head and pressure areproportional) and is transformed into the integral form to be able tocalculate the flow rate in a simple way.

Further preferably, the second equation may be a velocity equation inintegral form. This is preferably based on a hydromechanicaldifferential equation that in particular describes a torque balance andis converted into the integral form to be able to calculate the modelspeed in a simple manner.

For example, the first equation or volume flow equation can be used inthe following integral form:

$\begin{matrix}{Q_{mdl} = {\frac{1}{L_{hyd}}{\int}_{0}^{t}\left( {\left( {{a\omega^{2}} - {{bQ}_{mdl}\omega} - {cQ}_{mdl}^{2}} \right) - {R_{hyd}Q_{mdl}^{2}} - H_{static}} \right){dt}}} & {G11}\end{matrix}$

where

Q_(mdl) the flow rate of the centrifugal pump to be determined,

ω a speed or rotational frequency of the centrifugal pump (ω=2πn) ,

a, b, c are parameters that describe the hydraulic pump map (H(Q, ω)) bymeans of pump curves,

R_(hyd) the hydraulic resistance of the hydraulic system,

L_(hyd) the hydraulic inductance of the hydraulic system and

Hstatic is a geodetic head.

The numerical solution of this first equation G11 can be done by adiscrete-time implementation using the so-called forward Eulerintegration, where the conveying stream Q_(mdl) on the left side of theequation at time k+1 is calculated from the conveying flow Q_(mdl) onthe right side of the equation at time k. The numerically solvablediscrete-time form of the first equation can then be:

$\begin{matrix}{{Q_{mdl}\left( {k + 1} \right)} = {{Q_{mdl}(k)} + {\frac{1}{L_{hyd}}{\left( {\left( {{a{\omega^{2}(k)}} - {{{bQ}_{mdl}(k)}{\omega(k)}} - {{cQ}_{mdl}^{2}(k)}} \right) - {R_{hyd}{Q_{mdl}^{2}(k)}} - {H_{static}(k)}} \right) \cdot \Delta}t}}} & {G11}\end{matrix}$

Here Δt is the time interval between time k+1 and time k.

The model parameters a, b, c are known per se, since they represent thestatic mathematical relationship H=f(Q, ω) between delivery head H andflow rate Q for any given rotational speed win other words the so-calledpump curve that is regularly measured at the factory for centrifugalpumps and consists of the sum of all pump curves, i.e. curves H_(ω)=fQof constant speed that are specified by the manufacturer in thetechnical documentation of the pump. In contrast, the hydraulicresistance R_(hyd) of the system, the hydraulic inductance L_(hyd) ofthe system and its geodetic head Hstatic depend on the system itself,more precisely on its topology and condition, it being significantlydependent on the position of the valves in the system, so that itshydraulic resistance is variable.

Preferably, estimated values are used for the hydraulic resistanceR_(hyd) and the hydraulic inductance L_(hyd) at the beginning of themethod. By using the method according to the invention, any estimationerror is compensated.

In the case of a closed pipe network, as is the case for example in aheating system or cooling system with a heat transfer medium circulatingin a circuit, the geodetic head is zero, so that for this applicationH_(static)=0 can be set. The value for the geodetic head H_(static) can,for example, be manually set by a user on the control electronics of thecentrifugal pump if it is constant. However, it is also possible for thecontrol electronics to set the value for the geodetic head H_(static)itself, in particular to zero, based on an indication of the pipingnetwork or the application (heating system, cooling system) in which thecentrifugal pump is operated. In the case of a variable geodetic head,this must be measured or otherwise determined.

To be able to specifically specify the delivery head in addition to oras an alternative to the flow rate, the first equation (volume flowequation) can be separated into a first and second partial equation,where the first partial equation describes the static hydraulic pump mapfor calculating the delivery head and the second partial equation is thedynamic volume flow equation using the calculated delivery head. Thesecond partial equation can also be considered as the main equation asit retains integral form, whereas the first equation can be consideredas a secondary equation as it provides a term required in the mainequation.

For example, the first partial equation, hereafter Eq1a, and secondpartial equation, hereafter Eq1b can be used in the following form:

$\begin{matrix}{H_{mdl} = {{a\omega^{2}} - {{bQ}_{mdl}\omega} - {cQ}_{mdl}^{2}}} & {G11a}\end{matrix}$ $\begin{matrix}{Q_{mdl} = {\frac{1}{L_{hyd}}{\int}_{0}^{t}\left( {H_{mdl} - {R_{hyd}Q_{mdl}^{2}} - H_{static}} \right){dt}}} & {G11b}\end{matrix}$

where H_(mdl) is the head of the centrifugal pump to be determined, moreprecisely a model size.

As already explained for the first equation Eq. 1, the numericalsolution of the second partial equation Eq. 1b can also be carried outby a discrete-time implementation with the aid of the forward Eulerintegration, whereby the conveying current Q_(mdl) on the left-hand sideof the equation at time k+1 is derived from the conveying flow Q_(mdl)on the right side of the equation at time k. The numerically solvablediscrete-time form of the second partial equation G11b can then be:

G11b:

${Q_{mdl}\left( {k + 1} \right)} = {{Q_{mdl}(k)} + {\frac{1}{L_{hyd}}{\left( {{H_{mdl}(k)} - {R_{hyd}{Q_{mdl}^{2}(k)}} - {H_{static}(k)}} \right) \cdot \Delta}t}}$

Here Δt is the time interval between time k+1 and time k.

The first subequation Eq. 1b can also be implemented in discrete time:

H _(mdl)(k)=aω ²(k)−bQ _(mdl)(k)ω(k)−cQ _(mdl) ²(k)   G11a:

In terms of process technology, the two partial equations G11a, G11b canbe evaluated one after the other. Preferably, the first partial equationG11a is evaluated first, i.e. the delivery head H_(mdl) is calculatedbased on an initial flow rate value Q_(mdl)(k=1)=Q_(start) which can bezero, for example. Subsequently, based on the determined delivery headvalue H_(mdl) the second partial equation G11b is evaluated, i.e. thenew flow rate value Q_(mdl)(k+1) is determined.

In an alternative variant, or the evaluation of the first equation G11or its first partial equation G11a, the actual speed ω_(real) is used asthe rotational speed ω that can be supplied to the pump-motor model forthis purpose. This actual speed ω_(real) can be measured or calculatedby the motor control of the electric motor driving the centrifugal pump,which sets the torque in step a.

To ensure that the results are consistent, for the evaluation of thefirst equation Eq. 1 or its first partial equation Eq. la, the speed cocan be used. the model speed ω_(mdl) which was previously calculatedwithin the pump-motor model using the second equation or the speedequation G12. This is possible because the disturbance controllercalculating the disturbance signal manages to compensate very well forany speed error, so that the model speed and the real speed are thesame.

It should be noted that for the model-based determining the flow rate orthe head, the other quantity must always also be determined, at leastwithin the pump-motor model, but depending on whether the flow rate orthe head or both quantities are to be determined as part of the methodaccording to the invention, either only the flow rate or only the heador both quantities are output from the pump-motor model.

For example, the velocity equation can be used in the following integralform:

$\begin{matrix}{\omega_{mdl} =} & {G12}\end{matrix}$$\frac{1}{J}{\int}_{0}^{t}\left( {T_{mot} - \left( {{a_{t}Q_{mdl}\omega} - {b_{t}Q_{mdl}^{2}} - {c_{t}\frac{Q_{mdl}^{3}}{\omega}} + {v_{i}\omega^{2}} + {v_{s}\omega} - {I\frac{dQ}{dt}}} \right) + T_{D}} \right){dt}$

where

T_(mot) the mechanical torque of the motor (motor torque) of thecentrifugal pump,

T_(D) the calculated disturbance signal in the form of a moment(disturbance moment),

Q_(mdl) the flow rate of the centrifugal pump to be determined,

-   -   ω_(mdl) the model speed or rotational frequency of the        centrifugal pump (ω=2πn),    -   ω a speed or rotational frequency of the centrifugal pump        (ω=2πn),    -   a_(t), b_(t), c_(t) are parameters that describe the static        torque map (T(Q, ω)) of the centrifugal pump by means of torque        curves,    -   ν_(i) a quantity describing the friction between impeller and        medium,    -   ν_(s) a quantity describing the bearing friction,    -   J the mass inertia of the rotating components of the centrifugal        pump (impeller, shaft, rotor), and    -   I is the mass inertia of the pumped medium in the impeller.

The speed equation G12 describes in integral form a hydromechanicaldifferential equation in the manner of a torque balance in which thedeviation between the motor torque T_(mot) and the theoretical pumptorque T_(mdl) plus a modeling error-related disturbance torque T_(D) isintegrated. The motor torque T_(mot) is set by the motor control of theelectric motor driving the centrifugal pump to achieve the setpointspeed, or is modulated directly, and to this extent is known from themotor control.

For evaluating the second equation G12, as with the first equation G11,the speed can be taken as ω, the actual speed ω_(real), or the modelspeed ω_(mdl) can be used.

The second equation Eq. 2 can also be solved numerically by adiscrete-time implementation using forward Euler integration, where therotational speed ω_(mdl) on the left-hand side of the equation at timek+1 is calculated from the rotational speed ω_(mdl) on the right side ofthe equation at time k. The numerically solvable discrete-time form ofthe second equation G12 can then be:

$\begin{matrix}{{\omega_{mdl}\left( {k + 1} \right)} = {{\omega_{mdl}(k)} + {\frac{1}{J}{\left( {{T_{mot}(k)} - \left( {{a_{t}{Q_{mdl}(k)}{\omega(k)}} - {b_{t}{Q_{mdl}^{2}(k)}} - {c_{t}\frac{Q_{mdl}^{3}(k)}{\omega(k)}} + {v_{i}{\omega^{2}(k)}} + {v_{s}{\omega(k)}} - {I\frac{{Q(k)} - {Q\left( {k - 1} \right)}}{\Delta t}}} \right) + {T_{D}(k)}} \right) \cdot \Delta}t}}} & {G12}\end{matrix}$

Here is Δt is again the time interval between time k+1 and time k.

The theoretical pump torque T_(mdl) results from a model equation thatis described in the second equation Eq2 by the inner bracket expression.In it, the model parameters a_(t), b_(t), c_(t) are known per se, sincethey represent the static mathematical relationship T=f(Q, ω) betweenthe torque T and the flow Q for an arbitrary rotational speed ωIn otherwords, they describe the torque map which can be measured at the factoryfor centrifugal pumps and which consists of the sum of all torquecurves, i.e. curves T_(ω)=f of constant speed. The model parametersa_(t), b_(t), c_(t) are on the one hand subject to series dispersion,i.e. they differ slightly from centrifugal pump to centrifugal pump dueto tolerances, in particular by a few percent. On the other hand, theyare subject to change due to ageing, in particular due to bearing wearand deposits on the impeller. The quantity describing the frictionbetween impeller and medium ν_(i) and the quantity describing thebearing friction (viscous friction in the hydrodynamic plain bearing)ν_(s) can also be determined by measuring the centrifugal pump at thefactory and are known quantities in this respect. The mass inertia J canbe calculated or measured from design data of the centrifugal pump andis therefore also available from the manufacturer. The same applies tothe mass inertia I of the pumped medium in the impeller that is,however, negligibly low, so that the term

$I\frac{dQ}{dt}$

can be set to zero.

To simplify the calculation of the velocity equation G12, it can beseparated into a first and second partial equation G12a, G12b, where thefirst partial equation G12a describes the static hydromechanical pumpcharacteristic field (torque characteristic field) for calculating thetheoretical pump torque and the second partial equation G12b is thedynamic velocity equation using the calculated theoretical pump torque.The second partial equation can also be considered as the main equationin this case, since it keeps the integral form, whereas the firstequation can be considered as a secondary equation, since it provides aterm needed in the main equation.

For example, the first partial equation G12a and second partial equationG12b can be used in the following form:

$\begin{matrix}{T_{mdl} = {{a_{t}Q_{mdl}\omega} - {b_{t}Q_{mdl}^{2}} - {c_{t}\frac{Q_{mdl}^{3}}{\omega}} + {v_{i}\omega^{2}} + {v_{s}\omega} - {I\frac{dQ}{dt}}}} & {G12a}\end{matrix}$ $\begin{matrix}{\omega_{mdl} = {\frac{1}{J}{\int}_{0}^{t}\left( {T_{mot} - T_{mdl} + T_{D}} \right){dt}}} & {G12b}\end{matrix}$

where T_(mdl) is the theoretical pump torque of the centrifugal pump tobe calculated, more precisely a model quantity.

The numerical solution of the second partial equation Eq. 2b can againbe done by a discrete-time implementation using the forward Eulerintegration, where the rotational speed ω_(mdl) on the left side of theequation at time k+1 is calculated from the rotational speed ω_(mdl) onthe right side of the equation at time k. The numerically solvablediscrete-time form of the second partial equation G12b can then be:

$\begin{matrix}{{\omega_{mdl}\left( {k + 1} \right)} = {{\omega_{mdl}(k)} + {\frac{1}{J}{\left( {{T_{mot}(k)} - {T_{mdl}(k)} + {T_{D}(k)}} \right) \cdot \Delta}t}}} & {G12b}\end{matrix}$

The first subequation Eq. 2a can also be implemented in discrete time:

$\begin{matrix}{{T_{mdl}(k)} = {{a_{t}{Q_{mdl}(k)}{\omega(k)}} - {b_{t}{Q_{mdl}^{2}(k)}} - {c_{t}\frac{Q_{mdl}^{3}(k)}{\omega(k)}} + {v_{i}{\omega^{2}(k)}} + {v_{s}{\omega(k)}} - {I\frac{{Q(k)} - {Q\left( {k - 1} \right)}}{\Delta t}}}} & {G12a}\end{matrix}$

where the term

$I\frac{{Q(k)} - {Q\left( {k - 1} \right)}}{\Delta t}$

can also be left out. In terms of process technology, evaluation of thetwo partial equations of the velocity equation can be carried out oneafter the other. Preferably, the first partial equation G12a isevaluated first, i.e. the pump torque is calculated, on the one handusing an initial flow rate value Q_(mdl)(k=1)=Q_(start) which can bezero, for example, and on the other hand based on an initial speed valueω_(mdl)(k=1)=ω_(start) greater than zero. Subsequently, based on thedetermined pump torque T_(mdl) the second partial equation Eq2b isevaluated, i.e. the new model speed ω_(mdl)(k+1) is determined.

To calculate the disturbance signal, the difference between the actualspeed and the model speed may be fed to a controller containing at leastone integral component. For example, the controller may be an I, PI orPID controller as is commonly known in control engineering. Thedisturbance signal may be the output signal of the controller orcalculated from this controller output signal. The controller may beinitialized with the value zero. If there is no difference between themodel speed and the actual speed, the disturbance signal remainsunchanged. If the difference is greater than zero, the value of thedisturbance signal increases; if it is less than zero, the value of thedisturbance signal decreases. In this respect, the controller can bedescribed as a “disturbance controller” which compensates for thedeviation between the real pump and the pump model and brings the modelspeed into line with the actual speed. The controller output is thus ameasure of the (torque) deviation or disturbance of the model. Byevaluating this disturbance according to the invention, the model can bedynamically adjusted.

As mentioned above, in one embodiment, the output signal of thiscontroller may form the disturbance signal T_(D). Since this signalT_(D) is part of a torque equation, the physical quantity of thecontroller output is a torque or “disturbance torque,” because acontroller output quantity always has the dimension of the manipulatedvariable on which the controller acts. In another embodiment, thedisturbance signal may be formed by multiplying the output signal ofthis controller by the actual speed, so that this disturbance signalrepresents a power. Thus, in this case, the disturbance signal P_(D) maybe considered as a “disturbance power.” Thus, a basic idea of the methodaccording to the invention is to adjust the at least one modelparameter, or even several model parameters at the same time, in such away that no disturbance torque T_(D) and/or no disturbance power P_(D)is present. In other words, the pump-motor model is continuouslyadjusted so that it always replicates reality and compensates forexternal disturbance effects on the centrifugal pump as well as anymodel errors. The pump-motor model is therefore dynamic in this respect.

According to a further development of the method, the combination of thetwo embodiments mentioned is also possible. Thus, in step d. a firstdisturbance signal T_(D) and a second disturbance signal P_(D) can bedetermined by feeding the difference between the model speed and theactual speed to a controller containing at least one integral component,the output signal of this controller forming the first disturbancesignal T_(D) and the second disturbance signal P_(D) then being formedby multiplying the output signal of this controller by the actual speed.In other words, the second disturbance signal can be regarded ascalculated from the first disturbance signal. Two disturbance signalsT_(D), P_(D) are then present that can be further processed separatelyfrom each other and each offer the possibility of adjusting or trackingone or more model variables of the pump-motor model.

Preferably, a correction signal T_(D1 sin) is determined from thedisturbance signal T_(D) and used to adapt a model parameter of thepump-motor model. It is further possible that two or more correctionsignals T_(D1 sin), T_(D1 cos) are determined from the disturbancesignal T_(D) and each used to adjust a model parameter of the pump-motormodel. In this way, two or a number of different model parameterscorresponding to the number of correction signals can consequently beadjusted simultaneously. Finally, it is also possible that one, two oreven more correction signals T_(D1 sin), T_(D1 cos), P_(D1 sin),P_(D1 cos) are determined from each of the disturbance signals T,P_(DD), and that each correction signal T_(D1 sin), T, P,P_(D1 cos D1 sin D1 cos) is used to adjust one particular modelparameter R_(hyd), J, L_(hyd), c_(t) of the pump-motor model. Thisallows three, four or more model variables of the pump-motor model to beadjusted simultaneously and independently.

In principle, any of the correction signals can be used to adjust one ofthe model parameters. However, it should be noted that those correctionsignals which represent an active component, i.e. are in phase with theexcitation of the speed or torque, correct those model parameters whichpredominantly act on the active power. In contrast, correction signalsthat represent a reactive power, i.e. are 90° out of phase with theexcitation, can only correct model parameters that predominantlyinfluence the reactive power.

For example, the model parameter to be adjusted may be the hydraulicresistance R_(hyd) of the piping network or the model parameter c_(t).The hydraulic resistance R_(hyd) indicates the steepness of thecharacteristic curve of the piping system. It changes if the pipingsystem has controlled valves, as is the case in heating or coolingsystems, for example. Tracking the hydraulic resistance R_(hyd) in thepump-motor model is therefore of particular advantage to ensure theaccuracy of the head and/or flow rate determination. The model parameterc_(t) is subject to series variation from centrifugal pump tocentrifugal pump and also changes with the age of the centrifugal pump,whereas the other parameters a_(t) and b_(t) have no strong dependenceand remain almost constant. The model parameters R_(hyd), c_(t) affectthe active power. Therefore, in this case, it is provided that in stepe. the sine or cosine signal that is in phase with the excitation signalis used. In other words, in step e., the sine signal is used when theexcitation signal is also a sine signal, and the cosine signal is usedwhen the excitation signal is also a cosine signal.

To adjust both of the above-described model variables R_(hyd), c_(t) ina preferred embodiment, the hydraulic resistance R_(hyd) can be adjustedas a function of a first correction signal P_(D1 sin) formed from thesecond disturbance signal P_(D), and the model parameter c_(t) can beadjusted as a function of a first correction signal T_(D1 sin) formedfrom the first disturbance signal T_(D). However, the reverse is alsopossible, i.e. that the hydraulic resistance R_(hyd) is adapted as afunction of the first correction signal T_(D1 sin) formed from the firstdisturbance signal T_(D), and the model parameter c_(t) is adapted as afunction of the first correction signal P_(D1 sin) formed from thesecond disturbance signal P_(D). However, the former variant has theadvantage that the c_(t)—term

$c_{t}\frac{Q^{3}}{\omega}$

of the torque equation (Eq. 2) in the corresponding power equation dueto the multiplication with the speed (P=T·ω) only acts as c_(t)Q³ and isdropped out in the integration of this power equation. Furthermore, itis of course also possible that in one embodiment only one of the thesemodel parameters R_(hyd), c_(t) is adjusted and then either the firstcorrection signal T_(D1 sin) of the first disturbance signal T_(D), orthe first correction signal P_(D1 sin) of the second disturbance signalP_(D) is used for this purpose.

According to one embodiment, the model parameter to be adjusted can bethe mass inertia J of the centrifugal pump or the hydraulic inductanceL_(hyd) of the pipeline network. An adaptation or tracking of theinertia J of the centrifugal pump as a model parameter has the advantagethat ageing phenomena on the centrifugal pump, such as deposits on theimpeller (clogging) or bearing wear, can be detected, since theseincrease the inertia. If the model parameter “inertia” is thus increasedwithin the scope of the method, an indication, in particular maintenanceinformation, can be output on the centrifugal pump if a predeterminedlimit value is exceeded. An adaptation or tracking of the hydraulicinductance as a model parameter has the advantage that structuralchanges to the piping system can be detected, for example as a result ofa fault by which a network section is permanently cut off from the rest,or as a result of a conversion or extension of the pipe power network.The detection of an increasing or decreasing hydraulic inductance canalso be used to issue an indication at the centrifugal pump, forexample, for the purpose of checking the operating setting of thecentrifugal pump and/or to directly adjust the control of thecentrifugal pump, for example, by increasing or decreasing its referencespeed or a set control characteristic. These model parameters J,L_(hyd), influence the reactive power. Therefore, in this case, it isprovided that in step e. the sine or cosine signal that is 90° out ofphase with respect to the excitation signal is used. In other words, instep e., the cosine signal is used when the excitation signal is a sinesignal, and the sine signal is used when the excitation signal is acosine signal.

To adjust both these model variables J, L_(hyd) in a preferredembodiment, the inertia J can be adjusted as a function of a secondcorrection signal P_(D1 cos) formed from the second disturbance signalP_(D), and the hydraulic impedance L_(hyd) can be adjusted as a functionof a second correction signal T_(D1 cos) formed from the firstdisturbance signal T_(D). However, it is also possible the other wayround, i.e. that the inertia J is adjusted as a function of the secondcorrection signal T_(D1 cos) formed from the first disturbance signalT_(D), and the hydraulic impedance L_(hyd) is adjusted as a function ofthe second correction signal P_(D1 cos) formed from the seconddisturbance signal P_(D). Furthermore, it is of course also possiblethat in one embodiment only one of these model parameters J, L_(hyd) isadapted and then either the second correction signal T_(D1 cos) of thefirst disturbance signal T_(D), or the second correction signalP_(D1 cos) of the second disturbance signal P_(D) is used for thispurpose.

In one embodiment, it may further be provided that all fourabove-described model parameters R_(hyd), c_(t), J, L_(hyd) are eachadjusted simultaneously in dependence on the above-described correctionsignals T_(D1 sin), T_(D1 cos), P_(D1 sin), P_(D1 cos), for example.

the hydraulic resistance R_(hyd) as a function of the first correctionsignal P_(D1 sin) formed from the second disturbance signal P_(D), themodel parameter c_(t)as a function of the first correction signalT_(D1 sin) formed from the first disturbance signal T_(D)

the inertia J as a function of the second correction signal P_(D1 cos)formed from the second disturbance signal P_(D) and

the hydraulic impedance L_(hyd) as a function of the second correctionsignal T_(D1 cos) formed from the first disturbance signal T_(D).

In mathematical terms, step e. is a sine/cosine transformation that isperformed discretely on a processor. In the following, however, thecontinuous-time representation of the mathematical relationships is usedfor the sake of simplicity.

Preferably, the correction signal, or in the case of several correctionsignals of the respective correction signal, is determined by using asine or cosine signal with a multiple of the excitation frequency. If,for example, the excitation signal has the frequencyω t, then in thiscase the sine or cosine signal which is multiplied by the interferencesignal, or in the case of two interference signals by the respectiveinterference signal, also has this simple frequencyω t, hereinafter alsoreferred to as the fundamental frequency. However, it is also possible,alternatively or to obtain further correction signals, to additionallyuse a sine or cosine signal with double, triple or another nth multipleof the fundamental frequency, i.e. with a frequency 2ω, 3ω or nω t.However, since the amplitude of the correction signal is largest whenthe fundamental frequency is used, the use of a sine or cosine signalwith one times the excitation frequency, i.e. the fundamental frequency,is the preferred choice. As described above, in this case already twomodel parameters per disturbance signal (one model parameter when usinga sine signal with fundamental frequency and one when using a cosinesignal with fundamental frequency in step e.), i.e. four modelparameters for two disturbance signals (disturbance torque anddisturbance power). If, in addition, twice the fundamental frequency isused, two further model parameters can be adapted, and in the case oftwo disturbance signals even four.

In this case, the correction signals can be formed mathematically asfollows:

using the fundamental frequency of the excitation signal:

-   -   the first correction signal T_(D1 sin) of the first disturbance        signal T_(D):

$T_{D1\sin} = {\frac{1}{T}{\int}_{0}^{T}{T_{D} \cdot {\sin\left( {\omega_{A}t} \right)}}{dt}}$

-   -   the second correction signal T_(D1 cos) of the first disturbance        signal T_(D):

$T_{D1\cos} = {\frac{1}{T}{\int}_{0}^{T}{T_{D} \cdot {\cos\left( {\omega_{A}t} \right)}}{dt}}$

-   -   the first correction signal P_(D1 sin) of the second disturbance        signal P_(D):

$P_{D1\sin} = {\frac{1}{T}{\int}_{0}^{T}{P_{D} \cdot {\sin\left( {\omega_{A}t} \right)}}{dt}}$

-   -   the second correction signal P_(D1 cos) of the second        disturbance signal P_(D):

$P_{D1\cos} = {\frac{1}{T}{\int}_{0}^{T}{P_{D} \cdot {\cos\left( {\omega_{A}t} \right)}}{dt}}$

-   -   and using the nth multiple of the fundamental frequency of the        excitation signal:    -   a correction signal T_(Dn sin) of the first disturbance signal        T_(D):

$T_{D{n\sin}} = {\frac{1}{T}{\int_{0}^{T}{{T_{D} \cdot {\sin\left( {n\omega_{A}t} \right)}}dt}}}$

-   -   a correction signal P_(Dn cos) of the second disturbance signal        P_(D):

$P_{Dncos} = {\frac{1}{T}{\int_{0}^{T}{{P_{D} \cdot {\cos\left( {n\omega_{A}t} \right)}}dt}}}$

From a mathematical point of view, the calculation of the least one ormore correction signals is a type of Fourier analysis, but integrals areonly calculated for a few individual frequencies. These integrals can beconsidered as Fourier integrals.

It is also possible to use the DC component of the disturbance signal toadjust or track a specific model parameter.

Preferably, the adaptation of the or the corresponding model parameterR_(hyd), J, L_(hyd), c_(t) is carried out using a controller containingat least one integral component, to which the or the respectivecorrection signal T_(D1 sin), T_(D1 cos), P_(D1 sin), P_(D1 cos),wherein the controller output signal is multiplied by an initial valuefor the or the corresponding model parameter (R_(hyd), J, L, c_(hydt))to obtain the adjusted model parameter R_(hyd), J, L_(hyd), c_(t). Theinitial value may be a factory measured value (for inertia J or c_(t))or an average value assumed for the intended operation of thecentrifugal pump (for R_(hyd), L_(hyd)). The controller can be an I, PIor PID controller. Due to the integral component (I component) in thecontroller, it acts like an integrator.

The controller output signal can be understood as a correction factor Kfor the model parameter. The controller can be initialized with thevalue 1 at the beginning of the procedure, so that the controller outputsignal K=1 and the multiplication with the initial value results in theadjusted model parameter being equal to the initial value at thebeginning of the procedure, i.e. remaining unchanged. If the correctionsignal is zero, the controller output signal remains at K=1. However, ifthe correction signal is greater than 0, the correction factor Kincreases, and if the correction signal is less than 0, the correctionfactor K decreases. As a result of the multiplication of the correctionfactor K by the initial value, the model parameter is then increased ordecreased. The controller can thus be referred to as a “parametercontroller.” The advantage of this arrangement is that the controllercan be easily limited. For example, the correction factor can be limitedto a factor of 5, where permissible values can preferably be between ⅕and 5. This makes it possible to determine how far the value has movedaway from the initial assumption, i.e. the initial value.

It should be noted that, in the context of the present description, theterms “have,” “comprise” or “include” in no way exclude the presence ofother feature. Furthermore, the use of the indefinite article inrelation to a subject does not exclude its plural.

BRIEF DESCRIPTION OF THE DRAWING

Further features, characteristics, effects and advantages of theinvention will be explained in more detail below with reference toexamples or embodiments and the accompanying figures. The referencesigns contained in the figures retain their meaning from figure tofigure. In the figures, reference signs always denote the same or atleast equivalent components, areas, directions or locations. In thedrawing:

FIG. 1 is a schematic representation of a centrifugal pump within aclosed hydraulic system;

FIG. 2 is a signal flow diagram of a first embodiment of the methodaccording to the invention with singular model parameter adjustment;

FIG. 3 is a signal flow diagram with an embodiment of the pump-motormodel 9 in FIG. 2 ;

FIG. 4 is an embodiment of the disturbance controller 10 in FIG. 2 ;

FIGS. 5-8 show different versions of the parameter controller 12 in FIG.2 ;

FIG. 9 is a signal flow diagram of a second embodiment of the methodaccording to the invention with singular model parameter adjustment andmissing actual speed feed to the pump-motor model 9;

FIG. 10 is a signal flow diagram with an embodiment of the pump-motormodel 9 a in FIG. 9 with internal use of the model speed;

FIG. 11 is a signal flow diagram of a third embodiment of the methodaccording to the invention comprising a multi-model parameter adaptationand a single disturbance variable on the output side of the disturbancecontroller 10;

FIG. 12 is a signal flow diagram of a fourth embodiment of the methodaccording to the invention with multi-model parameter adaptation and twodisturbance variables on the output side of the disturbance controller10 a;

FIG. 13 is an embodiment of the disturbance controller 10 a in FIG. 12 ;and

FIG. 14 is a signal flow diagram showing an embodiment of the pump-motormodel 9 b in FIGS. 11 and 12 with multi-model parameter fitting.

SPECIFIC DESCRIPTION OF THE INVENTION

FIG. 1 shows a purely schematic representation of a centrifugal pump 3,4 within a closed hydraulic system 1 in which the centrifugal pump 3, 4circulates a fluid. The hydraulic system 1 may be, for example, aheating system or a cooling system for buildings, although forsimplicity system components such as a heating source or chiller, heatexchanger, hydraulic separator, valves, etc. are omitted. However, thehydraulic system 1 comprises a piping network 2 extending from thecentrifugal pump 3, 4 to a number of consumers (flow), such asradiators, heating circuits of a floor heating system or coolingcircuits of a cooled ceiling and extending from these consumers back tothe centrifugal pump 3, 4 (return). In this case, the centrifugal pump3, 4 is intended to convey a heat transfer medium, such as water, to theconsumers. Control valves, such as thermostatic valves or electrothermalactuators, are associated with these consumers to adjust the flow ratethrough the respective consumer or through a group of consumers. Due tothe varying degree of opening of these control valves, the hydraulicload 5 to be served by the centrifugal pump 3, 4 changes according tothe demand from the consumers, which for simplicity is symbolized inFIG. 1 by a single, but variable hydraulic resistance R_(hyd). Itdescribes the slope of the so-called pipe network parabola of thehydraulic system 1, generally also called system characteristic curve orsystem curve.

It should be noted that the hydraulic system may equally be an opensystem, as in the case of a borehole pump, a sewage-lift station or adrinking-water pressure-boosting system.

The centrifugal pump 3, 4 comprises a centrifugal pump 4 together withan electric motor drive and pump or control electronics 4 forcontrolling with or without feedback the electric motor that are alsoset up for carrying out the method according to the invention. Theelectric motor may, for example, be a three-phase, permanently excited,electronically commutated synchronous motor. The control electronics 4comprise a frequency converter for setting a specific speed of theelectric motor. In operation, the centrifugal pump 4 generates adifferential pressure between its suction and discharge sides, alsoreferred to as head H_(real) that, depending on the hydraulic resistanceR_(hyd) of the pipe network 2 connected to the centrifugal pump 4,results in a flow rate Q_(real).

A signal flow diagram illustrating the sequence of a first embodiment ofthe method according to the invention for determining the currentdelivery head H_(real) and/or the current delivery flow Q_(real) asaccurately as possible by calculation is shown in FIG. 2 . The methodcan be roughly divided into six process sections I to VI that areexplained individually below. The process sections I to IV basicallytake place simultaneously and are repeatedly executed cyclically oneafter the other as a result of their program-technical processing bysoftware in the control electronics 4, in particular at the clock speedof a processor not shown in the control electronics 4 on which theprocess according to the invention runs.

In the first process section I, a periodic excitation of the hydraulicsystem 1 takes place. In this embodiment, this takes place by applying aperiodic excitation signal f_(A) of a specific excitation frequencyω_(A)to a reference rotational speed n₀ of the centrifugal pump 3, 4 toobtain a modulated set rotational speed n_(soll) and thus to modulatethe actual rotational speed n_(real) of the centrifugal pump 3, inparticular to cause it to fluctuate periodically. It should be noted atthis point that in various places in the figures the rotationalfrequencyω is used instead of the rotational speed n that due to therelationshipω=2π n does however correspond to the rotational speed andis understood to be synonymous with it, which is why in the following werefer generally to the “rotational speed ω.”

The periodic excitation f_(A) has the effect of modulating thedifferential pressureΔ p of the centrifugal pump 3 or its delivery headH_(real) proportional thereto that, depending on the modulationamplitude and frequency, results in a signaling response of thehydraulic system 1 that in turn is reflected in the torque required toset the modulated setpoint speed n_(soll), and also in the electricalpower consumption of the centrifugal pump, from which the delivery flowQ can be determined. This basic principle is described in U.S. Pat. No.10,184,476, to which reference is hereby made.

The reference speed no can be an externally specified speed for thecentrifugal pump 3, 4 or a speed determined internally in the controlelectronics 4. It can, for example, originate from a characteristiccurve control upstream of the speed control that, for example, sets thedelivery head H as a function of the delivery flow Q according to adefined characteristic curve in the so-called HQ diagram, or result froman automatic control that sets the delivery head H as a function ofother criteria, e.g. the change in delivery flow dQ/dt.

For example, the excitation signal f_(A) can be a sinusoidal signal ofthe form f_(A)=n₁·sin(ω_(A)·t), where n₁ is the excitation amplitude andω_(A) is the excitation frequency. However, the excitation need not besinusoidal. Another periodic waveform such as a square wave, trapezoidalwave, triangular wave, sawtooth wave or shark fin waveform are alsopossible. The periodic excitation of the system 1 or application of theexcitation signal f_(A) to the reference speed no is done bysuperimposition in an adder 6, to which the reference speed no and theexcitation signal f_(A) are each supplied in terms of signals. Theoutput variable of this adder 6 is the modulated reference speedn_(soll)=n₀+n₁·sin(ω_(A)·t). This forms the input variable for thesecond process step II.

In this second method section II, the motor control 7 known per se iscarried out for setting the modulated setpoint speed n_(soll), forexample using a vectorial, in particular field-oriented control. Sincethe actual speed ω_(real) is the controlled variable in this case, it isdirectly available from the field-oriented control, either based on ameasurement by means of an encoder, by evaluating the voltage inducedback into the stator coils by the rotor magnetic field (back EMF) orbased on a calculation using a known algorithm for sensorless speedcontrol. The motor control 7 comprises at least one speed controller 8,to which the modulated reference speed n_(soll) is fed and whichdetermines the torque T_(mot) required to achieve the modulatedreference speed n_(soll) as a function of the deviation of the actualspeed ω_(real) from the reference speed n_(soll) or, of course,ω_(soll). The actual speed ω_(real) is thus also an input variable ofthe speed controller 8. The speed controller 8 may, for example, be a P,PI or PID controller, in which case the torque T_(mot) is themanipulated variable. It can also be a PI-R controller that has aresonance component at the excitation frequency ω_(A) to achieve thelowest possible control deviation.

The determined torque T_(mot) is then adjusted by the motor control 7 onthe drive of the centrifugal pump 3 that in FIG. 2 forms a physicalsystem component. Depending on this torque T_(mot), a corresponding(actual) speed ω_(real) of the centrifugal pump 3 results that thengenerates a delivery head H_(real) and, depending on the load 5 in theform of the hydraulic resistance R_(hyd), a corresponding delivery flowQ_(real). The determined actual speed ω_(real), is fed to the speedcontroller 8 to determine the deviation from the set speed n_(soll) andto adjust the torque T_(mot). Such a motor control 7 is known per se.

According to the invention, the determined torque To is further fed to amathematical pump-motor model 9 which simulates the hydromechanicalbehavior of the centrifugal pump 3. This is a third section III of themethod according to the invention and is part of a model-based operatingpoint determination device 13 that is implemented in the controlelectronics 4 and is set up to determine the delivery head H_(mdl)and/or the flow rate Q_(mdl) of the centrifugal pump 3 from thepump-motor model 9. In control terms, this pump-motor model 9 representsa so-called observer which ideally enables observation of all statevariables of the centrifugal pump 3, i.e. also non-measurable statevariables. In particular, the pump-motor model 9 enables an estimationof the actual head H_(real), the actual flow Q_(real) and the actualspeed ω_(real) in the form of their respective model quantities H_(mdl),Q_(mdl) and ω_(mdl), it also being referred to as the model speedω_(mdl).

One embodiment of the pump-motor model 9 is illustrated in FIG. 3 . Itcomprises a system of equations based on a first differential equationG11a, G11b and a second differential equation G12a, G12b, each of whichis transformed into an integral form to form a first and a secondintegral equation to simplify their calculation. The first integralequation Eq1a, Eq1b is based on a hydraulic differential equationdescribing a pressure balance in system 1 expressed in head. It forms avolumetric flow equation since it allows the calculation of the flowrate Q_(mdl). The second integral equation Eq2a, Eq2b is based on ahydromechanical differential equation describing a torque balance insystem 1 considering friction losses. It forms a velocity equation sinceit allows the calculation of the model speed ω_(mdl). The two integralequations are calculated successively in a discrete-time manner usingforward Euler integration.

To simplify the evaluation of the two integral equations, they are eachdivided into a static first partial equation G11a, G12a (secondaryequation) and a dynamic second partial equation G11b, G12b (mainequation) that has the integral form. In this case, the first partialequation G11a, G12a and then the second partial equation G11b, G12b areeach calculated in terms of signal technology, whereby the result of thesolution of the respective first partial equation G11a, G12a is used forthe calculation of the respective second partial equation G11b, G12b, asis made clear below with reference to FIG. 3 , which is why the firstpartial equations can be regarded as secondary equations to the secondpartial equations that in turn form the main equations due to theirintegral form.

In total, the system of equations thus consists of the following foursubequations G11a, G11b, G12a, G12b, where the first two subequationsG11a, G11b form a set describing the first integral equation, and thesecond two subequations G12a, G12b form a set describing the secondintegral equation. In the discrete-time implementation, the partialequations are as follows

$\begin{matrix}{{H_{mdl}(k)} = {{a{\omega^{2}(k)}} - {b{Q_{mdl}(k)}{\omega(k)}} - {c{Q_{mdl}^{2}(k)}}}} & {G11a}\end{matrix}$ $\begin{matrix}{{Q_{mdl}\left( {k + 1} \right)} = {{Q_{mdl}(k)} + {\frac{1}{L_{hyd}}{\left( {{H_{mdl}(k)} - {R_{hyd}{Q_{mdl}^{2}(k)}} - {H_{static}(k)}} \right) \cdot \Delta}t}}} & {G11b}\end{matrix}$ $\begin{matrix}{{T_{mdl}(k)} = {{a_{t}{Q_{mdl}(k)}{\omega(k)}} - {b_{t}{Q_{mdl}^{2}(k)}} - {c_{t}\frac{Q_{mdl}^{3}(k)}{\omega(k)}} + {v_{i}{\omega^{2}(k)}} + {v_{s}{\omega(k)}}}} & {G12a}\end{matrix}$ $\begin{matrix}{{\omega_{mdl}\left( {k + 1} \right)} = {{\omega_{mdl}(k)} + {\frac{1}{J}{\left( {{T_{mot}(k)} - {T_{mdl}(k)} + {T_{D}(k)}} \right) \cdot \Delta}t}}} & {G12b}\end{matrix}$

where

H_(mdl) the delivery head to be determined H_(mdl) of the centrifugalpump 3,

Q_(mdl) the flow rate of the centrifugal pump 3 to be determined,

ω a speed or rotational frequency of the centrifugal pump (ω=2πn) ,

ω_(mdl) the model speed of the centrifugal pump 3,

-   a, b, c are parameters that describe the hydraulic pump map (H(Q,    ω)) by means of pump curves,

R_(hyd) is the hydraulic resistance of the hydraulic system 1,

L_(hyd) the hydraulic inductance of the hydraulic system 1 and

H_(static) is a geodetic head,

T_(mdl) the theoretical pump torque of the centrifugal pump 3 to becalculated,

T_(mot) the mechanical torque of the motor (motor torque) of thecentrifugal pump,

T_(D) a calculated disturbance signal in the form of a moment(disturbance moment),

a_(t), b_(t), c_(t) are parameters describing the static torque map(T(Q, ω)) of the centrifugal pump 3 by means of torque curves,

ν_(i) a quantity describing the friction between impeller and medium,

ν_(s) a quantity describing the bearing friction,

J the mass inertia of the rotating components of the centrifugal pump 3(impeller, shaft, rotor), and

k is a discrete time and

Δt is the time interval between one time k and the next time k+1.

In the first partial equation G11a of the first integral equation,further pressure terms can be considered, if necessary, to further adaptthe pump-motor model 9 to reality. Furthermore, in the first partialequation G12a of the second integral equation G12 further terms (e.g.for friction) can be considered if necessary.

The pump-motor model 9 in FIG. 3 comprises three function blocks 9.1,9.2, 9.3. In the second function block 9.2 the main equation G11b of thefirst integral equation (volume flow equation) is evaluated.Furthermore, in the third function block 9.3, the main equation G12b ofthe second integral equation (velocity equation) is evaluated. Thesecond and third function block 9.2, 9.3 are preceded by the firstfunction block 9.1, in which the two secondary equations G11a, G12a(pressure and torque characteristics) of the integral equations areevaluated. The functional summary of the calculation of these twopartial equations G11a, G12a in the first function block 9.1 is donehere because both partial equations G11a and G12a need the actual speedωand the flow rate Q to be calculated. However, the partial equationsG11a and G12a could just as well be calculated in separate functionblocks in terms of signal technology.

The first partial equation G11a of the first integral equation (volumeflow equation) describes the speed-dependent relationship between flowrate Q and head H, or more precisely the pump characteristic diagram,i.e. for each speed co the dependence of the head H on the flow rate Q,this relationship being referred to as the pump curve Hω(Q). Along sucha pump curve Hω the speed w is constant. All pump curves Hω form thepump map H(ω, Q). The pump characteristic diagram H(ω, Q) is usuallymeasured at the factory and specified in the technical documentation ofa centrifugal pump 3. The model parameters a, b, c that mathematicallydescribe the pump curve H(ω, Q), are therefore known.

To calculate the model quantity H_(mdl) by means of the partial equationG11a in the first function block 9.1, the speedω and the flow rate Q arerequired. In the embodiment according to FIGS. 2 and 3 , the speedω isprovided as the actual speed ω_(real) is provided by the motor controlunit 7 or fed to the first function block 9.1. The calculated feed flowQ_(mdl) from the output of the second function block 9.2 is used as thefeed flow Q and is also supplied to the first function block 9.1,wherein the feed flow Q_(mdl) is zero at the start of the process or adefined initial value is used. The calculated model variable H_(mdl) isoutput at the output of the first function block 9.1 and thus also formsthe delivery head to be determined in accordance with the inventionH_(mdl)which is output at the output of the pump-motor model 9 as thefirst output variable.

In addition, the calculated delivery head model variable H_(mdl) istransferred to the second function block 9.2, in which it is used tocalculate the delivery flow Q_(mdl) by means of the second partialequation G11b of the first integral equation. For the evaluation of thispartial equation G11b, the hydraulic resistance R_(hyd), the hydraulicimpedance L_(hyd), the current flow rate Q_(mdl) and the geodetic headHstatic are also required.

The second partial equation G11b of the first integral equation is basedon the hydraulic differential equation:

${H\left( {n,Q} \right)} = {{R_{hyd}Q^{2}} + {L_{hyd}\frac{dQ}{dt}} + H_{static}}$

that describes the system characteristic curve of the pipeline network 2or the hydraulic system 1 that depends significantly on theposition/degree of opening of the valves on the consumer side, i.e. onthe hydraulic resistance R_(hyd).

The geodetic head H_(static) is the minimum head H that must be reachedin order for a flow (Q>0) to be possible at all. In closed hydraulicsystems, i.e. those pipe networks in which the pumped medium circulates,such as in a heating or cooling system, the geodetic head H_(static) iszero and can be neglected in this case. In the case of an open system,the geodetic head H_(static) can, for example, be measured or specifiedon the pump electronics 4 of the centrifugal pump by a user.

The hydraulic resistance R_(hyd) and the hydraulic impedance L_(hyd) areinitially unknown, since these parameters are part of the user'shydraulic system 1 that the pump manufacturer does not know. Thehydraulic inductance L_(hyd), together with the volume flow, is ameasure of the kinetic energy stored in the flowing water mass. Providedthat the system is not changed structurally, the hydraulic impedanceL_(hyd) consequently does not change either. In the embodiment accordingto FIGS. 2 and 3 , it can be determined by a simple estimation. Incontrast, the hydraulic resistance R_(hyd) changes dynamically duringoperation of the system 1 as a function of the demand of the consumers,in particular the heating or cooling demand, i.e. as a function of theposition of the control valves on the consumer side which adjust thevolume flow through the consumers. However, when the valves closecompletely, the inductance L_(hyd) also changes.

In the first embodiment, the hydraulic resistance R_(hyd)is a modelparameter of the pump-motor model 9 which is dynamically adaptedaccording to the invention. It is repeatedly redetermined by a parametercontroller 12 and fed to the pump-motor model 9, more specifically tothe second function block 9.2, to be used in partial equation Eq1b.Since the hydraulic resistance R_(hyd) is unknown at the beginning ofthe process, any initial value can be used for R_(hyd). This is becauseduring the procedure its value is corrected by the parameter controller12 towards the real value, as will be explained further below.

The volumetric flow value Q to be used in equation G11b is thevolumetric flow value that is valid at the current point in time k.Partial equation G11b can thus be evaluated and the new volumetric flowQ_(mdl)(k+1) can be determined. It thus represents the output signal ofthe second function block 9.2 as well as the second output variable ofthe pump-motor model 9.

The first part G12a of the second integral equation (velocity equation)describes the speed-dependent relationship between torque T and flowrate Q. It is therefore basically a torque equation. Like partialequation Eq. 1a, it requires the current rotational speed wand thecurrent flow rate Q(k). As explained for the individual equation G11a,the speedω is the actual speed supplied by the motor control 7 to thefirst function block 9.1 ω_(real) and as the current delivery flow Q thedelivery flow Q_(mdl)(k+1) from the output of the second function block9.2 last calculated with partial equation G11b is used.

The term ν_(i)ω² in partial equation Eq. 2a describes the frictionbetween impeller and medium, the term ν_(s)ω describes the bearingfriction losses resulting from the bearing of the pump or motor shaft.Both quantities ν_(i) and ν_(s) can be determined at the factory bymeasuring the centrifugal pump and are therefore known. Furthermore, theterm

$I\frac{dQ}{dt}$

describes the moment of inertia of the medium in the impeller. Due tothe comparatively small amount of pumped medium in the impeller, theterm is comparatively small and can be neglected.

$I\frac{dQ}{dt}$

is comparatively small and can be neglected.

The model parameters a_(t), b_(t) and c_(t) describe the physicalrelationship between the torque T, flow Q and speed win other words thetorque map T(ω, Q) of the centrifugal pump 3 formed from the individualtorque curves Tω (Q), whereby the speedω is constant along a torquecurve Tω (Q). Since, as previously stated, each pump is measured by themanufacturer and its hydraulic and hydromechanical pump characteristicsare known to the manufacturer, the model parameters a_(t), b_(t) andc_(t) are also known per se. In the present example, the model parameterc_(t) is a value that can change with time. Its initial value can alsobe determined at the factory by measuring the centrifugal pump 3.

The calculated model quantity T_(mdl) is also output at the output ofthe first function block 9.1 and transferred to the third function block9.3, in which it is used to calculate the model speed ω_(mdl) by meansof the second partial equation G12b of the second integral equation. Forthe evaluation of this partial equation G12b, the moment of inertia J,the motor torque T_(mot) and the value of a disturbance torque T_(D) arealso required that exists in the event of a deviation of the model speedfrom the actual speed, i.e. is greater than zero in terms of amount. Themoment of inertia J of the rotating components (shaft, rotor, impeller)of the centrifugal pump 3 can also be determined at the factory bymeasuring the centrifugal pump 3 or calculated from design data. Themotor torque T_(mot) is fed to the pump-motor model 9 or the thirdfunction block 9.3 by the motor control 7. Furthermore, the disturbancetorque T_(D) is determined by a disturbance controller 10 and is alsofed to the pump-motor model 9 or the third function block 9.3.

Partial equation G12b can thus be evaluated and the model speed ω_(mdl)determined. It thus represents the output signal of the third functionblock 9.3 as well as the third output variable of the pump-motor model9.

The equations of the pump-motor model 9 are continuously calculatedrepeatedly, in particular depending on the clock rate of the processorof the control electronics 4 on which this calculation is performed. Inthis process, a new flow rate value Q_(mdl) (k+1) or speed value ω_(mdl)(k+1) is calculated in each clock cycle from the flow rate value Q_(mdl)or speed valueω_(mdl) used in the previous clock cycle.

With the aid of the pump-motor model 9 (observer) the actual speed ofthe centrifugal pump 3 is estimated as the model speedω_(mdl) and fed toa disturbance controller 10 that also receives the actual speedω_(real)of the centrifugal pump 3. The disturbance controller 10 forms a fourthprocess section IV, compare FIG. 2 . The disturbance controller 10 formsa fourth process section IV, compare FIG. 2 . It first determineswhether and to what extent there is a deviation of the model speedω_(mdl) from the actual speedω_(real) and determines a disturbancesignal T_(D)from this deviation. In this respect, the disturbancecontroller 10 forms a disturbance signal calculation unit. It isresponsible for setting or controlling the model speedω_(mdl) so that itcorresponds to the actual speed ω_(real).

A first embodiment of the disturbance controller 10 is shown in FIG. 4 .It comprises a subtractor 14 which calculates the deviation(ω_(real)−ω_(mdl)) of the model speedω_(mdl) from the actualspeedω_(real) of the centrifugal pump 3, 4. This part of the disturbancecontroller 10, together with the pump-motor model 9, can be understoodas a “torque observer,” because a deviation of the model speedω_(mdl)from the actual speedω_(real) means a deviation of the model 9 fromreality, which manifests itself in a disturbance torque that in turn isresponsible for the speed deviation. Furthermore, the disturbancecontroller 10 comprises a controller 15 having an integral componentthat is here a PID controller. The calculated deviation or speeddifference is fed to this controller 15 and integrated based on theintegral component. The physical quantity of the controller output isdefined by the connected manipulated variable, so that the controlleroutput signal (manipulated variable of the controller) physicallycorresponds to a torque.

In the first embodiment of the disturbance controller 10, the controlleroutput signal directly forms the disturbance signal T_(D) that canaccordingly be regarded as the disturbance torque T_(D). If thespeedsω_(mdl), ω_(real), differ, then the pump-motor model 9 does notmatch reality. Thus, the disturbance controller 10 may also be referredto as a “disturbance observer,” The disturbance torque T_(D) acceleratesthe model speed ω_(mdl) when it is less than the actual speed ω_(real),and brakes the model speed ω_(mdl) when it is greater than the actualspeed ω_(real). In this way, the disturbance signal T_(D) compensatesfor a deviation of the pump-motor model 9 from reality. Such a deviationcan, for example, be caused by inaccurate parameter values, but can alsobe due to external disturbances, such as torque fluctuations due toparticles or bubbles in the pumped medium or due to changing bearingfriction.

The PID controller 15 of the disturbance controller 10 is initializedwith the value 0. If the speedsω_(real) and ω_(mdl) are identical, theirdeviation is zero and the disturbance signal T_(D)(disturbance torque)is constant or also zero at the beginning of the process. If there is anegative deviation between the speeds ω_(mdl) and ω_(real) i.e. that theactual speedω_(real) lags behind the model speed ω_(mdl), thedisturbance signal T_(D) falls. This can be interpreted to mean that inreality a disturbance torque (braking torque) is acting, as a result ofwhich the centrifugal pump 3 actually has a lower speed ω_(real) than itis estimated by the pump-motor model 9. In other words, losses (e.g.friction losses/bearing wear, higher hydraulic resistance, higherinertia force, etc.) act in reality.) that are not taken into account inthe (idealized) pump-motor model 9, so that the pump-motor model 9overestimates the model speed ω_(mdl). If there is a positive deviationbetween the speeds ω_(mdl) and ω_(real), i.e. that the modelspeedω_(mdl) is estimated to be lower than the actual speed ω_(real),the disturbance signal T_(D) increases steadily as a result of the Icomponent of the controller 15. A too low model speed ω_(mdl) can bepresent if the pump-motor model 9 models the centrifugal pump 3, 4together with the connected system 1 too lossy, if necessaryoveradjusted.

The disturbance signal T_(D) is then fed to an evaluation unit 11 andevaluated therein, which represents a fifth process section V. Theevaluation unit 11 according to FIG. 2 is set up to determine acorrection signal T_(D1 sin) from the interference signal T_(D). This isdone in such a way that the interference signal T_(D) is firstmultiplied by a sinusoidal signal whose frequency corresponds to themultiple of the excitation frequency ω_(A), i.e. the fundamentalfrequency of the excitation signal fA(t). The product thus formed isthen integrated over at least one period T of the excitation signalf_(A) to obtain the correction signal T_(D1 sin). Mathematically, thisis a sinusoidal transformation. The correction signal T_(D1 sin) canthus be determined as follows:

$T_{D1sin} = {\frac{1}{T}{\int_{t}^{t + T}{{{T_{D}(t)} \cdot {\sin\left( {\omega_{A}t} \right)}}dt}}}$

The correction signal T_(D1 sin) is then fed to a parameter controller12 that is set up to carry out an adjustment of a model parameter as afunction of the correction signal T_(D1 sin). In the embodimentaccording to FIG. 2 , the model parameter to be adjusted is (only) thehydraulic resistance R_(hyd) of the pipe network 2.

A first embodiment of the parameter controller 12 is shown in FIG. 5 .It comprises a controller 17 with integral component to which thecorrection signal T_(D1 sin) is fed. The controller 17 is implementedhere as a PID controller. The output signal of this controller 17represents a correction factor K. The controller 17 is initialized withthe value 1 as one of the first steps of the method, so that thecorrection factor K initially has the value 1. The parameter controller12 further comprises a multiplier 19 which multiplies the correctionfactor K by an initial value of the model parameter R_(hyd).Consequently, if the correction factor K=1, the initial value is notcorrected so that the model parameter R_(hyd) is equal to the initialvalue. If the correction signal T_(D1 sin) is zero, the correctionfactor K remains unchanged. If the correction signal T_(D1 sin) isgreater than zero, the correction factor K is increased as a result ofthe integral component of the controller 17. If the correction signalT_(D1 sin) is less than zero, the correction factor K is decreased as aresult of the integration of the correction signal T_(D1 sin). The modelparameter R_(hyd) is consequently dynamically adapted, in particular“controlled with feedback,” by the parameter controller 12, thecorrection factor K indicating as a manipulated variable the extent ofthe deviation of the model parameter R_(hyd) from the initial value.

The correction factor K thus generally makes it possible to obtainfurther information about the centrifugal pump 3, 4 or the pipelinenetwork 2, such as information about ageing/wear of the centrifugal pump3, deposits on the impeller (clogging) or a fault in the pipelinenetwork. This makes it possible to monitor the condition of thecentrifugal pump 3, 4. If the correction factor K exceeds or falls belowa predetermined limit value, an error message, a warning and/ormaintenance notice can be issued.

The parameter controller 12 may further comprise a correction factorlimitation 18 which limits the correction factor K to an upper and/orlower limit value, for example to the upper value 5 or to the lowervalue ⅕, so that the permissible range of values for the model parameterto be adjusted is at most five times and one fifth of the initial value.The correction factor limiter 18 is thus located signal-wise between thecontroller 17 and the multiplier 19. The correction factor limiter 18prevents the model 9 from moving too far away from the real system, forexample, due to temporarily incorrect measured values. If, for example,the flow rate Q=0, the resistance R_(hyd)would have to be infinitelylarge. This means that this condition would never be reached byintegration. Conversely, it would then also take a very long time toreturn from infinity to another operating point. However, since theresult does not change significantly at very low volume flows, it makessense to limit the resistance R_(hyd). It can also be assumed for othermodel parameters that they can only change within a certain range.Otherwise, there may be another error, e.g. a measurement error.

Further, the parameter controller 12 may include a linearization unit 20such that the parameter controller 12 exhibits the same behavior forincrease as for decrease and the disturbance signal TD1 sin becomesproportional to the change in flow rate.

The model parameter R_(hyd), adjusted if necessary by the parametercontroller 12, is then fed to the pump-motor model 9. The pump-motormodel 9 then uses the adjusted model parameter in the second functionblock 9.2 to calculate the delivery flow Q_(mdl).

FIGS. 9 and 10 show a second embodiment of the pump-motor model 9 a. Itdiffers from the first embodiment in that no actual speed ω_(real) isfed to the pump-motor model 9 a from the motor control 7. Instead, themodel speed ω_(mdl) calculated internally in the previous cycle is usedin the pump-motor model 9 a for the individual equations G11a, G12a, forwhich the output of the third function block 9.3 is fed back to theinput of the first function block 9.1, see FIG. 10 . This is possiblebecause the disturbance controller 10 is able to compensate very wellfor any speed error.

The individual sections I-VI of the method according to the invention,which can also be regarded as functions, are summarized once again inthe following table:

Procedure sec. Function block Function I Speed Periodic excitation of areference specification speed II Motor control Speed control anddetermining actual speed and torque III Pump-motorCalculation/observation of speed, head model and flow rate IV FaultCalculating a disturbance signal; controller controller with highbandwidth, or a bandwidth of at least one decade above the excitationfrequency; ensures that model speed corresponds to actual speed VEvaluation Calculating one or more correction unit signals from thedisturbance signal VI Parameter Model parameter adjustment as acontroller function of the correction signal

This method improves the accuracy of the flow rate and/or headdetermination, since any disturbance torque T_(D) is counteracted by thedisturbance controller 10 and the subsequent parameter adjustment in theparameter controller 12, thereby reducing the noise in the flow rateand/or head signal compared to the prior art approach. Thus, the signalquality can be improved or a lower excitation amplitude than in theprior art can be used for the excitation signal while maintaining thequality, or a subsequent smoothing by filtering can be reduced, so thata faster reaction of the centrifugal pump 3, 4 to system state changesor disturbances in the hydraulic pipeline network 2 can take place. As aresult of the adjustment of the model parameter during operation of thepump 3, 4, any inaccuracies in the pump-motor model 9 are alsocompensated for, which may be due to a scattering of the modelparameters in series production and/or wear due to ageing, for exampleof the bearings of the centrifugal pump 3.

In principle, only the hydraulic resistance R_(hyd) needs to be trackedto determine the flow rate Q, at least if the other model parameters areknown from a measurement, estimate, calculation, etc., since R_(hyd) isthe only dynamically variable parameter. Nevertheless, the hydraulicresistance R_(hyd) could also be determined in another way and fed tothe pump-motor model 9. The method according to the invention is thusnot limited to tracking the hydraulic resistance R_(hyd) with theevaluation unit 11 and the parameter controller 12. Rather, a singleother parameter can also be tracked, such as the moment of inertia J,the hydraulic impedance L_(hyd) or the parameter c_(t). In the case ofthe moment of inertia J, the parameter controller 12 in FIG. 2 or 9 isformed by the moment of inertia controller 12′ from FIG. 6 , in the caseof the hydraulic impedance L_(hyd) by the impedance controller 12″ fromFIG. 7 and in the case of the parameter c_(t) by the c_(t) controller12″′ from FIG. 8 . In each of these three cases, the evaluation unit 11also outputs a different correction signal, as will be explained below.

However, to improve the accuracy of the flow rate determination, inparticular also in case of series dispersion (model parameters fordifferent pumps of the same series may differ due to manufacturing andtolerances) as well as over the several years of operation of thecentrifugal pump 3, 4, i.e. in case of ageing effects, theabove-described further parameters of the pump-motor model 9 can betracked in addition to the hydraulic resistance. It is then alsopossible to obtain further information about, for example, the wear ofthe pump 3, 4.

FIG. 11 shows a third variant of the method according to the invention.It differs from the first and second variants essentially in that theevaluation unit 11 a receives the actual speedω_(real) and calculatesseveral correction signals, whereby each correction signal can be usedto adjust a single model parameter, so that a number of model parametersof the pump-motor model 9 b corresponding to the number of correctionsignals can be adjusted simultaneously. In this regard, each correctionsignal is calculated in a correction signal calculation unit 11.1, 11.2,all of which are part of the evaluation unit 11 a. From the actual speedω_(real), the evaluation unit 11 a can calculate a second disturbancesignal P_(D). Further, the evaluation unit 11 a may calculate one ormore correction signals from both the first disturbance signal T_(D) andthis second disturbance signal P_(D) respectively.

The evaluation unit 11 a according to FIG. 11 is set up to perform adiscrete sine/cosine transformation of the disturbance signal T_(D) ordisturbance torque T_(D) at the fundamental frequencyω_(A) of theexcitation signal f_(A)(t). On the one hand, by integrating the productof the disturbance signal T_(D) and a sinusoidal signal with the thisfundamental frequencyω_(A), a first correction signal T_(D1 sin) whichrepresents an active component (or real component) and is in phase withthe excitation signal f_(A) (t), and a second correction signalT_(D1 cos) which represents a blind part (or imaginary part) and isorthogonal to the excitation signal f_(A) (t). In addition, the DCcomponent T_(D0) of the disturbance signal T_(D) can be calculated as athird correction signal. These three correction signals can be used toadapt three parameters of the pump-motor model 9 b, since they woulddisappear in a non-faulty model. Mathematically, the three correctionsignals can be T_(D1 sin), T_(D1 cos), T_(D0) can be represented by thefollowing integrals, each of which is calculated in one of thecorrection signal calculation units 11.1, 11.2:

${T_{D1sin} = {\frac{1}{T}{\int_{t}^{t + T}{{{T_{D}(t)} \cdot {\sin\left( {\omega_{A}t} \right)}}{dt}}}}}{T_{D1cos} = {\frac{1}{T}{\int_{t}^{t + T}{{{T_{D}(t)} \cdot {\cos\left( {\omega_{A}t} \right)}}{dt}}}}}{T_{D0} = {\frac{1}{T}{\int_{t}^{t + T}{{T_{D}(t)}dt}}}}$

In the same way even further frequencies can be excited and evaluated.One receives thereby per frequency nω_(A)t two further correctionsignals T_(Dn sin), T_(Dn cos) from the first interference signal T_(D)that can be calculated in corresponding correction signal calculationunits 11.1, 11.2:

${T_{Dnsin} = {\frac{1}{T}{\int_{t}^{t + T}{{{T_{D}(t)} \cdot {\sin\left( {n\omega_{A}t} \right)}}{dt}}}}}{T_{Dncos} = {\frac{1}{T}{\int_{t}^{t + T}{{{T_{D}(t)} \cdot {\cos\left( {n\omega_{A}t} \right)}}dt}}}}$

These can be used to track two other model parameters.

As already mentioned, the evaluation unit 11 a is further set up tocalculate a second disturbance signal P_(D) and to perform a discretesine/cosine transformation of this second disturbance signal P_(D) atthe fundamental frequency of the excitation signal f_(A) (t). For thispurpose, the product of the first disturbance signal or the disturbancetorque T_(D) and the actual speed ω_(real) is first calculated thatrepresents a power P_(D)=T_(D)·ω_(real) which can be referred to as“disturbance power” in analogy to the disturbance torque T_(D).

Alternatively to the calculation of the second disturbance signal P_(D)in the evaluation unit 11 a, this calculation can be performed in thedisturbance controller 10 a. FIGS. 12 and 13 illustrate such anembodiment variant. Thus, the actual speed does not have to be suppliedto the evaluation unit. As can be seen from FIG. 13 , the disturbancecontroller 10 a used in FIG. 12 in this case additionally comprises amultiplier 16 which multiplies the output signal of the controller 15,i.e. the disturbance torque T_(D), by the actual speed ω_(real) and thusprovides a disturbance power P_(D) at its output. The disturbance torqueT_(D)is then the first disturbance signal T_(D) and the disturbancepower P_(D) is the second disturbance signal P_(D), both of which aretransferred by the disturbance controller 10 a to the evaluation unit 11a so that it does not have to calculate the second disturbance signalP_(D).

From the second disturbance signal P_(D), the evaluation unit 11 acalculates, by integrating the product of the second disturbance signalP_(D) and a sinusoidal signal having this fundamental frequencyω_(A), afourth correction signal P_(D1 sin) which represents an active part (orreal part) and is in phase with the excitation signal f_(A) (t), and afifth correction signal P_(D1 cos) representing a blind part (orimaginary part) and being orthogonal to the excitation signal f_(A) (t).In addition, the DC component P_(D0) of the second disturbance signalP_(D) can be calculated as the sixth correction signal. Thus, threefurther correction signals P_(D1 sin), P_(D1 cos), P_(D0) can bedetermined by forming the following integrals, which is performed ineach case in one of the correction signal calculation units 11.1, 11.2:

${P_{D1sin} = {\frac{1}{T}{\int_{t}^{t + T}{{{P_{D}(t)} \cdot {\sin\left( {\omega t} \right)}}{dt}}}}}{P_{D1cos} = {\frac{1}{T}{\int_{t}^{t + T}{{{P_{D}(t)} \cdot {\cos\left( {\omega t} \right)}}{dt}}}}}{P_{D0} = {\frac{1}{T}{\int_{t}^{t + T}{{P_{D}(t)}dt}}}}$with P _(D) =T _(D)(t)·ω_(real)(t)

In the same way, further frequencies can be excited and evaluated. Onereceives thereby per frequency nω_(A)t two further correction signalsP_(Dn sin), P_(Dn cos) from the second interference signal P_(D)

${P_{Dnsin} = {\frac{1}{T}{\int_{t}^{t + T}{{{P_{D}(t)} \cdot {\sin\left( {n\omega_{A}t} \right)}}{dt}}}}}{P_{Dncos} = {\frac{1}{T}{\int_{t}^{t + T}{{{P_{D}(t)} \cdot {\cos\left( {n\omega_{A}t} \right)}}dt}}}}$

which can be used to track two additional model parameters.

Of course, the evaluation unit 11 a does not necessarily have tocalculate all the above-described correction signals. Rather, this canbe done as required and desired.

The correction signals T_(D1 sin), T_(D1 cos), P_(D1 sin), P_(D1 cos),T, P_(D0D0) etc. calculated by the evaluation unit 11 are then fed tothe parameter controller 12 a that is set up to adjust one modelparameter per correction signal. This is done in single parametercontrollers 12.1, 12.2, etc., each of which is supplied with aparticular correction signal. Thus, six model parameters can be adjustedsimultaneously by this parameter controller 12 a. The parametercontroller 12 thus consists, more precisely, of a number of individualparameter controllers 12.1, 12.2, each of which may have a structure asin FIG. 5, 6, 7 or 8 , and each of which specifies a model parameter. InFIG. 5 this is the hydraulic resistance R_(hyd), in FIG. 6 the inertia Jof the rotating components of the centrifugal pump 3, in FIG. 7 thehydraulic impedance L_(hyd) and in FIG. 8 the model parameter c_(t). Theparameter controller 12 in FIG. 5 differs from the other parametercontrollers 12′, 12″, 12″′ of FIGS. 6 to 8 only in that it has alinearisation unit 20. In addition, each parameter controller 12, 12′,12″, 12″′ has a controller 17, 17 a, 17 b, 17 c with an integralcomponent which, for example, can be as a PID controller, a multiplier19, 19′, 19″, 19″′ for multiplying the respective correction factor K,K_(a), K_(b), K_(c) by the corresponding initial value of the respectivemodel parameter R_(hyd), J, L_(hyd), c_(t), and optionally a correctionfactor limiter 18, 18′, 18″, 18′″. The operation of each parametercontroller 12, 12′, 12″, 12′″ is as previously described with respect tothe first embodiment.

In principle, each individual correction signal can be used for thetracking of a model parameter. However, it should be noted that signalswhich represent an active component, i.e. signals which are in phasewith the excitation of the pump speed—i.e. the sinusoidal signals in thecase of sinusoidal excitation—adjust those model parameters whichpredominantly act on the active power. This is the case with thehydraulic resistance R_(hyd) and the model parameter c_(t), which is whythe parameter controllers 12, 12″ are fed the correction signalsT_(D1 sin) and P_(D1 sin) for these model parameters in FIGS. 5 and 8 .However, it does not matter which of these parameter controllers 12,12″′ receives the correction signal T_(D1 sin) and which receives thecorrection signal P_(D1 sin). The correction signal supply can beinterchanged to this extent.

In contrast, those correction signals which represent reactive power,i.e. are 90° out of phase with the excitation of the pump speed, i.e.the previously mentioned correction signals T_(D1 cos) and P_(D1 cos),should adapt such model parameters which predominantly influence thereactive power. This is the case with the inertia J and the hydraulicimpedance L_(hyd), which is why the parameter controllers 12′, 12″ aresupplied with the correction signals T_(D1 cos) and P_(D1 cos) for thesemodel parameters in FIGS. 6 and 7 . Again, it does not matter which ofthese parameter controllers 12′, 12″ receives the correction signalT_(D1 cos) and which receives the correction signal P_(D1 cos). Thecorrection signal supply can also be interchanged in this respect.

Experiments have shown that the following assignment of the correctionsignals T_(D1 sin), T_(D1 cos), P_(D1 sin), P_(D1 cos), T_(D0), P_(D0)to the model parameters is advantageous:

-   -   T_(D1 sin) to adjust the model parameter R_(hyd)    -   T_(D1 cos) to adjust the model parameter L_(hyd)    -   P_(D1 sin) to adjust the model parameter c_(t)    -   P_(D1 cos) to fit the model parameter J    -   T_(D0) to adjust the model parameter ν_(s)    -   P_(D0) to adjust the model parameter ν_(i)

However, other combinations are also possible. According to thisassignment, the individual correction signals can be fed to that singleparameter controller 12.1, 12.2, etc. which adjusts the correspondinglyassigned model parameter.

The output signals of the single parameter controllers 12.1, 12.2, etc.,i.e. the adjusted model parameters, are then made available to thepump-motor model 9 b, whose signal flow diagram FIG. 14 shows. Thepump-motor model 9 b can then use these new values of the modelparameters to calculate the model speedω_(mod), the flow rate Q_(mdl)and the head H_(mdl). For this purpose, the model parameter c_(t) is fedto the first function block 9.1, the two model parameters R_(hyd) andL_(hyd) are fed to the second function block 9.2 and the model parameterJ is fed to the third function block 9.3, within each of which the newmodel parameter values are then used in the corresponding partialequations G11b, G12a, G12b.

It should be noted that the above description is given by way of exampleonly for purposes of illustration and in no way limits the scope ofprotection of the invention. Features of the invention indicated as“may,” “exemplary,” “preferred,” “optional,” “ideal,” “advantageous,”“optionally,” “suitable” or the like are to be regarded as purelyoptional and likewise do not limit the scope of protection that isdefined exclusively by the claims. To the extent that the abovedescription recites elements, components, process steps, values orinformation having known, obvious or foreseeable equivalents, suchequivalents are embraced by the invention. Likewise, the inventionincludes any changes, variations or modifications to embodiments thatinvolve the substitution, addition, alteration or omission of elements,components, process steps, values or information, so long as the basicidea of the invention is maintained, regardless of whether the change,variation or modification results in an improvement or deterioration ofan embodiment.

Although the above description of the invention mentions a plurality ofphysical, non-physical or procedural features in relation to one or morespecific example of the invention, these features may also be used inisolation from the specific example of the invention, at least to theextent that they do not require the mandatory presence of furtherfeatures. Conversely, these features mentioned in relation to one ormore specific embodiment may be combined with each other and withfurther disclosed or non-disclosed features of shown or non-shownembodiments as desired, at least to the extent that the features are notmutually exclusive or do not lead to technical incompatibilities.

1. A method of determining the delivery flow and/or the delivery head of a speed-controlled centrifugal pump, wherein a reference speed or a torque of the centrifugal pump is acted upon by a periodic excitation signal of a specific excitation frequency to achieve a modulated setpoint speed, the method comprising the steps of: a. determining and adjusting a torque required to achieve the modulated reference speed or adjustment of the modulated torque, b. determining the actual speed of the centrifugal pump, c. calculating a model speed with the aid of a mathematical pump-motor model simulating the behavior of the centrifugal pump within a hydraulic system, d. calculating at least one disturbance signal from a deviation of the model speed from the actual speed of the centrifugal pump, e. determining at least one correction signal by integrating the product of the disturbance signal and a sine or cosine signal with a multiple of the excitation frequency over at least one period of the excitation signal, f. adapting at least one model parameter of the pump-motor model as a function of the correction signal, and g. calculating the flow rate and/or the head using the adapted pump-motor model.
 2. The method according to claim 1, wherein the pump-motor model comprises at least a first equation in integral form for calculating the flow rate and a second equation in integral form for calculating the model speed, and these two equations are repeatedly cyclically evaluated.
 3. The method of claim 2, wherein the first equation is used in the following integral form: $\begin{matrix} {{Q_{mdl} = {\frac{1}{L_{hyd}}{\int_{0}^{t}{\left( {\left( {{a\omega^{2}} - {bQ_{mdl}\omega} - {cQ_{mdl}^{2}}} \right) - {R_{hyd}Q_{mdl}^{2}} - H_{static}} \right){dt}}}}}{or}} & {G11} \end{matrix}$ $\begin{matrix} {{Q_{mdl}\left( {k + 1} \right)} = {{Q_{mdl}(k)} + {\frac{1}{L_{hyd}}{\left( {\left( {{a{\omega^{2}(k)}} - {b{Q_{mdl}(k)}{\omega(k)}} - {c{Q_{mdl}^{2}(k)}}} \right) - {R_{hyd}{Q_{mdl}^{2}(k)}} - {H_{static}(k)}} \right) \cdot \Delta}t}}} & {G11} \end{matrix}$ where Q_(mdl) the flow rate of the centrifugal pump, ω a speed or rotational frequency of the centrifugal pump (ω=2πn), a, b, care parameters that describe the hydraulic pump map (H(Q, ω)) by means of pump curves, R_(hyd) the hydraulic resistance of the hydraulic system, L_(hyd) the hydraulic inductance of the hydraulic system Hstatic is a geodetic head, k is a discrete time and Δt is the time interval between one time k and the next time k+1.
 4. The method according to claim 2 wherein the first equation (G11) is used in the form of the following two partial equations (G11a, G11b) which are calculated repeatedly one after the other: $\begin{matrix} {H_{mdl} = {{a\omega^{2}} - {bQ_{mdl}\omega} - {cQ_{mdl}^{2}}}} & {G11a} \end{matrix}$ $\begin{matrix} {{Q_{mdl} = {\frac{1}{L_{hyd}}{\int_{0}^{t}{\left( {H_{mdl} - {R_{hyd}Q_{mdl}^{2}} - H_{static}} \right){dt}}}}}{or}} & {G11b} \end{matrix}$ $\begin{matrix} {{H_{mdl}(k)} = {{a{\omega^{2}(k)}} - {b{Q_{mdl}(k)}{\omega(k)}} - {c{Q_{mdl}^{2}(k)}}}} & {G11a} \end{matrix}$ $\begin{matrix} {{Q_{mdl}\left( {k + 1} \right)} = {{Q_{mdl}(k)} + {\frac{1}{L_{hyd}}{\left( {{H_{mdl}(k)} - {R_{hyd}{Q_{mdl}^{2}(k)}} - {H_{static}(k)}} \right) \cdot \Delta}t}}} & {G11b} \end{matrix}$ where H_(mdl) is the delivery head of the centrifugal pump. Q_(mdl) the flow rate of the centrifugal pump, ω a speed or rotational frequency of the centrifugal pump (ω=2πn), a, b, care parameters that describe the hydraulic pump map (H(Q, ω)) by means of pump curves, R_(hyd) the hydraulic resistance of the hydraulic system, L_(hyd) the hydraulic inductance of the hydraulic system, Hstatic a geodetic head k is a discrete time and Δt is the time interval between one time k and the next time k+1.
 5. The method according to claim 2, wherein the second equation is used in the following integral form: $\begin{matrix} {\omega_{mdl} = {\frac{1}{J}{\int_{0}^{t}{\left( {T_{mot} - \left( {{a_{t}Q_{mdl}\omega} - {b_{t}Q_{mdl}^{2}} - {c_{t}\frac{Q_{mdl}^{3}}{\omega}} + {v_{i}\omega^{2}} + {v_{s}\omega} - {I\frac{dQ}{dt}}} \right) + T_{D}} \right){dt}{or}}}}} & {G12} \end{matrix}$ $\begin{matrix} {{\omega_{mdl}\left( {k + 1} \right)} = {{\omega_{mdl}(k)} + {\frac{1}{J}{\left( {{T_{mot}(k)} - \left( {{a_{t}{Q_{mdl}(k)}{\omega(k)}} - {b_{t}{Q_{mdl}^{2}(k)}} - {c_{t}\frac{Q_{mdl}^{3}(k)}{\omega(k)}} + {v_{i}{\omega^{2}(k)}} + {v_{s}{\omega(k)}} - {I\frac{{Q(k)} - {Q\left( {k - 1} \right)}}{\Delta t}}} \right) + {T_{D}(k)}} \right) \cdot \Delta}t}}} & {G12} \end{matrix}$ where T_(mot) the mechanical torque of the motor (motor torque) of the centrifugal pump, T_(D) the calculated disturbance signal in the form of a moment (disturbance moment), Q_(mdl) the flow rate of the centrifugal pump, ω_(mdl) the model speed or rotational frequency of the centrifugal pump (ω=2πn), ω a speed or rotational frequency of the centrifugal pump (ω=2πn), a_(t), b_(t), c_(t) are parameters describing the static torque map (T(Q, ω)) of the pump by means of torque curves, ν_(i) a quantity describing the friction between impeller and medium ν_(s) a quantity describing the friction in the bearing J the mass inertia of the rotating components of the centrifugal pump (impeller, shaft, rotor), The mass inertia of the pumped medium in the impeller, k is a discrete time and Δt is the time interval between one time k and the next time k+1.
 6. The method according to claim 2 wherein the second equation is used in the form of the following two partial equations (G12a, G12b) which are calculated successively, cyclically repeated: $\begin{matrix} {T_{mdl} = {{a_{t}Q_{mdl}\omega} - {b_{t}Q_{mdl}^{2}} - {c_{t}\frac{Q_{mdl}^{3}}{\omega}} + {v_{i}\omega^{2}} + {v_{s}\omega} - {I\frac{dQ}{dt}}}} & {G12a} \end{matrix}$ $\begin{matrix} {\omega_{mdl} = {\frac{1}{J}{\int_{0}^{t}{\left( {T_{mot} - T_{mdl} + T_{D}} \right){dt}{or}}}}} & {G12b} \end{matrix}$ $\begin{matrix} {{T_{mdl}(k)} = {{a_{t}{Q_{mdl}(k)}{\omega(k)}} - {b_{t}{Q_{mdl}^{2}(k)}} - {c_{t}\frac{Q_{mdl}^{3}(k)}{\omega(k)}} + {v_{i}{\omega^{2}(k)}} + {v_{s}{\omega(k)}} - {I\frac{{Q(k)} - {Q\left( {k - 1} \right)}}{\Delta t}}}} & {G12a} \end{matrix}$ $\begin{matrix} {{b{\omega_{mdl}\left( {k + 1} \right)}} = {{\omega_{mdl}(k)} + {\frac{1}{J}{\left( {{T_{mot}(k)} - {T_{mdl}(k)} + {T_{D}(k)}} \right) \cdot \Delta}t}}} & {G12} \end{matrix}$ where T_(mdl) a pump torque of the centrifugal pump T_(mot) the mechanical torque of the motor (motor torque) of the centrifugal pump, T_(D) the calculated disturbance signal in the form of a moment (disturbance moment), Q_(mdl) the flow rate of the centrifugal pump, ω_(mdl) the model speed or rotational frequency of the centrifugal pump (ω=2πn) , ω a speed or rotational frequency of the centrifugal pump (ω=2πn), a_(t), b_(t), c_(t) are parameters describing the static torque map (T(Q, ω)) of the pump by means of torque curves, ν_(i) a quantity describing the friction between impeller and medium ν_(s) a quantity describing the friction in the bearing J the mass inertia of the rotating components of the centrifugal pump (impeller, shaft, rotor), Idis the mass inertia of the pumped medium in the impeller, k is a discrete time and Δt is the time interval between one time k and the next time k+1.
 7. The method according to claim 1, wherein the difference between the model speed and the actual speed is fed to a controller containing at least one integral component, the output signal of this controller forming the disturbance signal or the disturbance signal being formed by multiplying the output signal of this controller by the actual speed.
 8. The method according to claim 1, wherein in step d. a first disturbance signal and a second disturbance signal are determined by supplying the difference between the model speed and the actual speed to a controller containing at least one integral component, and the output signal of this controller forms the first disturbance signal and the second disturbance signal is formed by multiplying the output signal of this controller by the actual speed.
 9. The method according to claim 1, wherein two or more correction signals are determined from the disturbance signal or from each of the disturbance signals from the disturbance signal or from each of the disturbance signals, and each correction signal is used to adapt in each case a specific model parameter of the pump-motor model.
 10. The method according to claim 1, wherein the model parameter is the hydraulic resistance of the system or the parameter, and in step e. the sine or cosine signal is used which is in phase with the excitation signal.
 11. The method according to claim 8, wherein the hydraulic resistance is adjusted in dependence of a first correction signal formed from the second disturbance signal and/or that the parameter is adjusted in dependence of a first correction signal formed from the first disturbance signal.
 12. The method according to claim 1, wherein the model parameter is the mass inertia of the centrifugal pump or the hydraulic inductance of the system and in step e. that sine or cosine signal is used which is 90° out of phase with the excitation signal.
 13. The method at least according to claim 8, wherein the mass inertia of the centrifugal pump is adjusted as a function of a second correction signal formed from the second disturbance signal, and/or in that the hydraulic inductance of the system is adjusted as a function of a second correction signal formed from the first disturbance signal.
 14. The method according to claim 1, wherein the adaptation of the model parameter is carried out using a controller containing an integral component, to which the correction signal is supplied, the controller output signal being multiplied by an initial value for the model parameter to obtain the adjusted model parameter.
 15. A centrifugal pump having a centrifugal pump, an electric motor driving it and control electronics for controlling with or without feedback the electric motor, wherein the control electronics are set up to carry out the method according to claim
 1. 